[UPSC CSE 2016] Thermodynamics (Q73, 10M)

Write down van der Waals' equation of state for n moles of a gas and calculate the temperature at which 5 moles of the gas at 5\ \mathrm{atm} pressure will occupy a volume of 20 litres. Given, R=8.31\times10^7\ \mathrm{erg\,mol^{-1}\,K^{-1}}, a=1.34\times10^{12}\ \mathrm{dyne\,cm^4\,mol^{-2}}, b=31.2\ \mathrm{cm^3\,mol^{-1}} and 1\ \mathrm{atm}=1.013\times10^6\ \mathrm{dyne\,cm^{-2}}.